Hi Atli,
Welcome and thanks for reaching out!
By default, the Month View displays the current month, even if you are on the last day of the month. Week View may be a better default display option for you if you’d like to display the events for the current week, without displaying anything before it. You can change the default calendar by heading to Event Settings>Display>Default View and Save Changes.
If you are interested in customizing the Month View, our Themer’s Guide is a great place to start. I would recommend looking at the templates related to the Month View, and in particular month/loop-grid.php.
I hope this helps! Please let me know if you have any other questions on this topic!
Thanks,
Jaime